Kotze-Pereira transformation: Difference between revisions
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[[File:Kotze-Pereira.png|thumb|Visual representation of the KP-Tansform]]
The '''Kotze-Pereira transformation''' ('''KP transform''') converts scored ballots into Approval ballots, which allows any Approval PR method to be run on scored ballots. Because the score winner will always have the most approvals after the transformation, a PR method that elects the approval winner in the single-winner case will also elect the score winner in the single-winner case when converted to a score method using the transformation. Score methods using this transformation are also generally
==Explanation==
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==Scale Invariance example for RRV==
[[Reweighted Range Voting]] is one example of a method
Let's say we have 5 candidates to elect and there are multiple A and B candidates, and we have the following approval ballots.
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900 ballots: B1, B2
Imagine A1, A2, B1, A3 are already elected. The new weighted total approvals for A4 would be 1800 x 1/4 = 450. For B2 it would be 900 x 1/2 = 450. This is the exact tie we want. So
== Notes ==
Using the "ranked KP transform" on Score ballots (converting them into Approval ballots which are then converted into ranked ballots, with approved candidates ranked 1st and all others last) and running this through [[Smith-efficient]] [[Condorcet methods]] yields a [[Smith set]] with only the candidates who originally had the most points i.e. the [[Score voting]] winner.
Something similar to the KP transform can be done using randomness: if a voter approves a candidate with a probability proportional to their utility from that candidate, then with probability approaching 1 with many voters, the candidate will have the same [[approval rating]] as they would if every voter had simply scored that candidate.
One way to visualize the KP transform is as follows: imagine that for each voter, 9 additional voters are added to the election, whose ballots are treated as "under the control of" that voter. If the voter decided to make 8 of the 10 ballots under their control approve their favorite candidate, while not doing anything with the remaining 2, then this would be equivalent to them giving that candidate an 8 out of 10 on a rated ballot. Thus, the KP transform helps with [[scale invariance]].
The KP transform often improves or at least doesn't worsen a voting method that it is applied to, but this isn't always the case. For example, [[SMV]] depends on being able to spend an entire ballot even if it didn't give full support to the winner.
The connection that the KP transform shows between Approval and Score ballots can most clearly be seen when the Score ballots are set to a scale of 0 to 1 (with in-between decimals allowed), because a voter who gives a middling score to a candidate is seen to be giving them a fractional approval.
The online community [https://www.reddit.com/r/SimDemocracy SimDemocracy] uses a form of KP-transform with SPAV (Jefferson), called "SPSV" ([[Sequential Proportional Score Voting]]) for its parliamentary elections<ref>{{cite web |url=https://www.reddit.com/r/SimDemocracy/wiki/pr_the_constitution_of_simdemocracy#wiki_article_28_-_appendix |access-date=2022-02-23 |title=The Constitution of r/SimDemocracy}}</ref>. A custom build voting tool is used to hold elections and requires a reddit account<ref>{{cite web |url=https://github.com/jonathanvdc/res-publica |title=Res Publica}}</ref>.
==Further Reading==
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